Transition From Elementary to Secondary School Mathematical - PowerPoint PPT Presentation

Transition From Elementary to Secondary School Mathematical concepts and processes February 2020 Direction de la formation générale des jeunes Ministère de l’Éducation et de l’Enseignement supérieur

The presenters Geneviève Dupré Person in charge of Mathematics curriculum Direction de la formation générale des jeunes M inistère de l’Éducation et de l’Enseignement supérieur Raymond Nolin Elementary school teacher at the Commission scolaire de Montréal seconded to the Ministère for the elementary school mathematics curriculum Annie Dubois Secondary school mathematics teacher at the Commission scolaire des Découvreurs seconded to the Ministère for the secondary school mathematics curriculum

Participants Elementary school Secondary school Elementary school Secondary school education consultants education consultants teachers teachers Elem.-Sec. ECs Others

Presentation outline 1. Objectives 2. Methodology for gathering information 3. Presentation of results 4. Thoughts and ideas

Objectives 1 The goal of the questionnaire and of this presentation

“. . . identify the mathematical concepts and processes that students find the most difficult at the end of Elementary Cycle Three. . . . support teachers in their professional practices so they can help students transition from elementary to secondary school . . . ” Mathematics curriculum team 2019, Questionnaire Arrimage primaire-secondaire, Concepts et processus mathématiques (Transition From Elementary to Secondary School: Mathematical Concepts and Processes), Introduction «

Methodology for gathering information 2 Process

Steps in the process 1. Identify the key concepts and processes that help students transition from elementary to secondary school 2. Create a questionnaire 3. Open the questionnaire in September 2019 4. Invite participants through the mailing list: Quoi de neuf en mathématique ? (What’s new in Mathematics?) 5. Close the questionnaire on November 29, 2019

Information gathering tool Research Questionnaire (Google Forms) Vocabulary for various Sociodemographic Geometry and Arithmetic Algebra Analytic Geometry Probability Statistics mathematical concepts data Measurement and processes Spatial sense and Understanding real analyzing situations School board numbers involving geometric Answers to statements in each section were figures provided using a Likert-type scale: 1 Very good understanding Understanding Analyzing situations Level of education operations involving Good understanding involving measurement real numbers Poor understanding Very poor understanding Not observed Operations involving real numbers 1 A Likert-type scale is an attitude scale consisting of a series of declarative statements for which respondents express an opinion (Fortin & Gagnon, 2016).

47 school boards and the private school system

375 total respondents 224 94 at the elementary level at the secondary level 45 12 at both levels no level indicated

Presentation of results 3 For each section of the questionnaire

Complete results

Types of slides used for the presentation of results

Arithmetic 3.1

Arithmetic: Understanding real numbers Represents a fraction and verifies whether two fractions are equivalent 80,0 66,2 70,0 57,6 56,8 60,0 Percentage 50,0 43,2 42,4 40,0 33,8 30,0 20,0 10,0 0,0 Elementary Secondary Total Primaire Secondaire Very good or good Poor or very poor Très bien ou bien maitrisé Peu ou très peu maitrisé understanding understanding

Arithmetic: Understanding operations involving real numbers ◉ Determines numerical equivalencies using relationships between operations (the commutative, associative and distributive properties) ○ Poor or very poor understanding: 72.6%

Arithmetic: Understanding operations involving real numbers Translates a situation using a sequence of operations in accordance with the order of operations 80,0 68,5 70,0 60,0 54,8 50,9 49,1 Percentage 45,2 50,0 40,0 31,5 30,0 20,0 10,0 0,0 Elementary Secondary Total Primaire Secondaire Very good or good Poor or very poor Très bien ou bien maitrisé Peu ou très peu maitrisé understanding understanding

Arithmetic: Operations involving real numbers ◉ Determines in writing the sum of two natural numbers of up to 4 digits ○ Good or very good understanding: 96.7% ◉ Determines in writing the difference between two natural numbers of up to 4 digits whose result is greater than 0 ○ Good or very good understanding: 94.8%

Arithmetic: Operations involving real numbers Approximates the result of an operation 80,0 70,0 60,2 58,6 60,0 52,9 47,1 Percentage 50,0 41,4 39,8 40,0 30,0 20,0 10,0 0,0 Elementary Secondary Total Primaire Secondaire Very good or good Poor or very poor Très bien ou bien maitrisé Peu ou très peu maitrisé understanding understanding

Arithmetic: Operations involving real numbers Determines in writing the quotient of a four-digit natural number and a two-digit natural number and expresses the remainder of a division as a decimal that does not go beyond the second decimal place 80,0 70,0 63,1 58,7 60,0 53,4 Percentage 46,6 50,0 41,3 36,9 40,0 30,0 20,0 10,0 0,0 Elementary Secondary Total Primaire Secondaire Very good or good Poor or very poor Très bien ou bien maitrisé Peu ou très peu maitrisé understanding understanding

Arithmetic: Operations involving real numbers Adds and subtracts fractions when the denominator of one fraction is a multiple of the denominator of the other fraction 80,0 70,0 61,5 57,9 60,0 50,0 50,0 Percentage 50,0 42,1 38,5 40,0 30,0 20,0 10,0 0,0 Elementary Secondary Total Primaire Secondaire Very good or good Poor or very poor Très bien ou bien maitrisé Peu ou très peu maitrisé understanding understanding

Arithmetic: Operations involving real numbers ◉ Determines the divisibility of a number by 2, 3, 4, 5, 6, 8, 9 and 10 ○ Poor or very poor understanding: 55.4%

Arithmetic: Operations involving real numbers Multiplies a natural number by a fraction and a fraction by a natural number 80,0 70,0 62,5 55,5 60,0 50,6 49,4 Percentage 50,0 44,5 37,5 40,0 30,0 20,0 10,0 0,0 Elementary Secondary Total Primaire Secondaire Very good or good Poor or very poor Très bien ou bien maitrisé Peu ou très peu maitrisé understanding understanding

Arithmetic: Operations involving real numbers Performs mentally and in writing operations with decimals (up to two places) 80,0 70,0 60,5 55,6 60,0 51,9 48,1 Percentage 50,0 44,4 39,5 40,0 30,0 20,0 10,0 0,0 Elementary Secondary Total Primaire Secondaire Very good or good Poor or very poor Très bien ou bien maitrisé Peu ou très peu maitrisé understanding understanding

Arithmetic: Operations involving real numbers Switches, as needed, from one way of writing numbers to another 80,0 70,0 70,0 60,0 55,1 55,1 Percentage 50,0 44,9 44,9 40,0 30,0 30,0 20,0 10,0 0,0 Elementary Secondary Total Primaire Secondaire Very good or good Poor or very poor Très bien ou bien maitrisé Peu ou très peu maitrisé understanding understanding

Algebra 3.2

Algebra ◉ Determines the missing term in an equation ○ Poor or very poor understanding: 55.7%

Any comments regarding arithmetic and algebra?

Geometry and Measurement 3.3

Geometry and Measurement Spatial sense and analyzing situations involving geometric figures Tests Euler’s relation on convex polyhedrons 80,0 71,7 70,0 60,0 53,3 50,7 49,3 46,7 Percentage 50,0 40,0 28,3 30,0 20,0 10,0 0,0 Elementary Secondary Total Primaire Secondaire Very good or good Poor or very poor Très bien ou bien maitrisé Peu ou très peu maitrisé understanding understanding

Geometry and Measurement Analyzing situations involving measurements Establishes relationships between units of time: second, minute, hour, day 80,0 70,0 62,0 60,0 54,5 50,4 49,6 Percentage 45,5 50,0 38,0 40,0 30,0 20,0 10,0 0,0 Elementary Secondary Total Primaire Secondaire Very good or good Poor or very poor Très bien ou bien maitrisé Peu ou très peu maitrisé understanding understanding

Analytic Geometry 3.4

Analytic Geometry ◉ Locates points in a Cartesian plane, based on the types of numbers studied ( x - and y -coordinates of a point) ○ Good or very good understanding: 91.6%

Probability 3.5

Probability ◉ Uses fractions, decimals or percentages to quantify a probability ○ Poor or very poor understanding: 58.4%